I thought about it some more and I believe it to be something like this: the air pressure inside the tire can support a certain amount of weight per PSI of tire pressure. The tire casing will deform until it reaches a point where enough surface area is making contact with the ground to support the weight of the bike and rider. This also means that if you increase the tire pressure the contact patch shrinks and if you decrease the tire pressure the contact patch increases. So, if you are not changing the tire pressure inside the tire but changing the tire size the amount of pressure inside the tire remains the same to hold up the weight of the rider and bike so the contact patch will remain the same regardless of the size of the tire.
Wider mountain bike tires, because they are wider, allow you to run a lower tire pressure than you would if you run a narrower tire. This is because the wider tire increases the contact area available so you now can run less pressure to increase traction (tire conforms to road irregularities better) with less worry about pinch flats.
Cars run wider tires for sporting purposes because you can get much more sideways loading on even your garden variety economy car than your average car can put into forward motion. Look at dragsters. They run tall, narrow tires in the rear under low pressures. This gives them a long, narrow contact patch for the best traction possible for acceleration because they have much more enging power than traction and they are trying to get as much traction for forward motion as possible. Road racers don't win races by all-out forward acceleration, for the most part, but by being able to corner hard. That's why they run wide tires on race cars. Mind you, they don't run rediculously wide tires on race cars because they also need to accelerate out of turns and brake hard going into it. Sports cars on the road go with wide tires more as a fad than anything else.
http://auto.howstuffworks.com/question506.htm To answer the question about how 30 PSI in your car tires holds up the weight of your two ton car, HowStuffWorks.com explains:
Notice that tire width doesn't factor in to the equation other than as a way to give you the measurements of the contact patch itself.